THE ATTRACTION OF THE HIMALAYA

Dr. J. de GRAAFF HUNTER

MEMBERS of the Himalayan Club will not be surprised at the above title ; but many of them will not have in mind exactly the subject with which the article is to deal. Attraction is a compendious term which includes many very different meanings. Here it is to be used in a very special sense : and while this may at first sight appear prosaic, it leads to ideas which have a very absorbing interest to some minds.

It is the physical gravitational pull of the Himalaya which will be discussed here and the inferences which observation results make possible. This attraction is a property of all matter, as was first recognized by Newton. The special interest of the Himalaya in this respect is due to their unique magnitude both in height and horizontal extent. In the first place the result of Himalayan attraction was recognized by geodetic surveyors. Sir George Everest, after whom the highest peak on earth has been named, was concerned in India from 1818 to 1843 with the measurements of precise triangulation to form the basis of mapping in India. Before triangulation can be properly reduced, reasonable knowledge of the general form and dimensions of the earth is required. In Everest's day such knowledge was not very precise, and accordingly a primary object of his work was to determine the magnitude of the earth from his observations. His problem was much complicated by Himalayan attraction.

The phenomenon of gravity is so ubiquitous as to be a commonplace. So much so that the majority of people simply accept it without question and do not enquire further into its origin or results. It is merely accepted that things are heavy or light as the case may be. It is not always recognized that the weight of a body varies by a half per cent, according as the body is near the equator or near the poles : and also that it is one-tenth per cent, less at a height of two miles above the earth than it is at the surface.

The force of gravity defines the vertical and is the preponderant factor in determining the general shape of the earth. The forces of attraction of a body of the size and density of the earth are so great that the shape essentially adjusts itself approximately to what it would be if its material were a simple fluid. The strength of no known substance is sufficient to enable it to remain in any other configuration. As an example, the weight of a column of granite of one square inch cross section three miles high is 8.36 tons—the same as its crushing strength (6 to 10 tons per sq. inch). Isolated columns of rocks do not occur at the earth's surface, and occasional peaks rise to greater height than this, Mount Everest itself reaching a height of 5| miles. The highest general level for a great extent also occurs in the Himalaya and reaches just this figure of three miles which considerations of strength have just shown to be the natural limit.

The height of three miles is formidable enough as a surface feature, but is only a small fraction of the earth's radius, so that in a generalized sense it t^an be stated that the earth is a spheroid—a figure not quite a sphere whose polar axis is less by one part in 300 than its equatorial axis. The statement is much more precise if the sea-level surface is considered instead of the actual surface. This sea-level surface is manifest in all ocean areas and it can be pictured in land areas if hypothetical channels, along which the ocean waters might flow, be imagined to exist. It is important to grasp this idea of the sea- level surface—what is scientifically known as the geoid—for it serves as the natural datum to which all terrestrial heights are referred. Most people are well accustomed to the statement that a mountain height is so many feet above sea-level, while not considering exactly what is meant. The precise meaning is that the height is measured vertically from the geoid—of which most people have never heard.

For the statement of height to have a full meaning, it is necessary to know the form of the geoid. This it is the work of the geodesist to determine, and it may be said at once that the geoid does not differ greatly from a spheroid—the figure developed by rotating an ellipse about its minor axis. Were the earth composed of fluid it would naturally take up a spheroidal form under the influence of the mutual attraction of its constituent particles and the forces of rotation. Actually it does not quite do this, and as has been seen above great areas exist of elevation as great as three miles above the geoid : and the geoid itself diverges from the spheroid by amounts which may perhaps reach 500 feet (up and down). In the limited regions where its form has been carefully investigated, the divergence is as much as 50 feet. A contributory cause to this divergence is the attraction of the topographical features of the earth, and the Himalaya form a very important example.

Early in his work Everest recognized that the Himalaya would exercise a disturbing effect. The disturbance is to be perceived as follows. In the first place high-class triangulation is executed— Everest had his great arc extending from Cape Comorin at the southern, extremity of India along meridian 78° up to Banog, in the neighbourhood of Mussoorie. The triangulation is controlled by several baselines which fix its scale : and with an assumed spheroid—fitting the geoid as closely as knowledge of the day allows—the latitude and longitude of all the stations of the triangulation may be calculated,

At selected stations the latitude is also observed astronomically by means of the stars. In this way two values of latitude of each of a number of stations are arrived at, one the geodetic latitude, the other the astronomic latitude.

A little consideration will show that the geodetic latitude depends on the spheroid assumed as a basis for the computation of the triangulation. If a somewhat different spheroid were selected, the values of latitude derived would be different. Consider it in this way, The triangulation effectively gives the length between any two of its stations : for example, two stations on the same meridian may work out to be 1,000 miles apart. If we measure 1,000 miles from a starting point of given latitude along a meridian on any spheroid we arrive at another point whose latitude is determinate—the latitude being merely the inclination of the normal to the spheroid, or spheroidal vertical to its equatorial plane. Clearly with a smaller spheroid we should encompass a greater range of latitude.

With the astronomic latitude the case is quite different: for here we find the inclination of the actual geoidal vertical—as revealed by a spirit bubble—to the plane at right angles to the axis of rotation of the earth. This is a perfectly definite quantity involving no assumption.

Horizontal Himalayan Attraction.—The two values of the latitude accordingly show the tilt of the geoid to the assumed spheroid what has been called the " deviation of vertical " or the ⁶⁴ plumb-line deflection." The two would agree if the geoid and spheroid were coincident. Values of these deviations at three points along his arc were known to Everest. Naturally his first procedure was to modify his assumed spheroid to reduce the deviations as far as possible. After this had been done residual deviation remained : and these he attributed to Himalayan attraction. The attraction might be expected to disturb the direction in which a plumb-line would hang compared with its direction if the Himalaya were absent. The plumb-bob would be pulled towards the north by different amounts at different stations depending on their distance from the Himalaya : and this was the result which observation actually displayed.

The next matter of interest was to see whether the amounts of the deflection at the several points agreed with what could be calculated from the known distribution of mass in the Himalaya. In 1852 Everest invited the co-operation of the mathematician, Archdeacon Pratt of Calcutta, who made the first calculations of Himalayan attraction. Pratt very soon found that the agreement was in no way perfect and that the computed effect of the Himalaya at distant points was much greater than deflection actually found. This discordance provided the starting point of a most interesting investigation as to the structure of the Himalaya, which—extended to all other mountains-—is very much alive to-day.

Work of Pratt and Airy.—Everest and Pratt had not very much data on which to build—actually three points at approximate intervals of 400 miles on longitude 78°, Kaliana, Kalianpur and Darmagida at approximate latitude 29|°, 24° and 18°. Still, they were quite enough to show that at points more than 100 miles distant from the Himalayan southern boundary, the expected Himalayan attraction was to a great extent cancelled by some other cause. In Pratt's day there was a widespread belief that the interior of the earth—the portion at depth greater than, say, 100 miles—was molten. So it was not unnatural to imagine that the crust of the earth was floating on the liquid core. Such a crust would collapse under the forces of gravity unless supported : and it was only a step further to imagine that individual features were supported by flotation, much in the manner that the ice on a frozen sea is supported.

Sir George Airy, then Astronomer Royal, also investigated the question : and both he and Pratt put forward hypotheses which to this day are current, associated with their names. Since then the word " isostasy," coined by Button of the U. S. Geological Survey in 1892; has been used to denote a state of affairs in which either hypothesis is embraced. In Pratt's isostasy as extended later it is supposed that below any topographical feature there is an anomaly of density uniformly distributed to such a depth as 70 miles, and such as to make the total mass above this depth of a column extending to the earth's surface proportional to its cross section. Thus in the case of a plateau three miles high the density of underlying matter is imagined to be below average by three-seventieths of average surface density. In the case of the sea a corresponding excess of density is now hypothecated by the supposition of isostasy : though this was not done by Pratt himself. Airy's isostasy was somewhat different in that he considered that the mountains floated precisely as ice-bergs do on the seas : that is they had roots of material less than average crust density, and the higher the mountain the deeper the roots.

Both Pratt's and Everest's hypotheses were developed in accord with two main ideas (a) fluid interior of the earth, (b) inability of the crust to support large features by its own rigidity. • Having been stated (about 1860), they were rather lost sight of for a number of years. They had given a reasonable explanation of the observed fact of attraction, and moreover, while not explaining how the Himalaya came into being, at least made their elevated existence natural. Geological evidence suggested that mountains had been formed by lateral compression generally attributed to the cooling down of the earth and contraction of its core, whereby the crust became too large for it. Pratt's work showed that in the case of the Himalaya at least the final result was one of almost hydrostatic equilibrium-a result not to be expected if mountains were simply squeezed into existence.

Burrard's Deductions.-—Nearly half a century later the matter was re-opened by Sir Sidney Burrard (late Surveyor-General of India). By this time the observational data were much increased : moreover the knowledge of the Himalaya themselves and their extent and altitude was vastly greater. It may be recalled that Mount Everest itself was only found in 1850 to be the highest mountain discovered on earth, and that the height 29,002 feet familiar now to so many, was attributed to it in 1853. Depths in the Indian Ocean were now also much more accurately known. Deflection results in the fringe of the Himalaya themselves made manifest the attraction of the Himalaya while showing that even there some compensating (defective) attraction was at work. In 1901 Burrard reviewed the results of latitude observations at 159 stations. He calculated the attractional effect of all topography to a distance exceeding 2,000 miles, and inferred the existence of a hidden chain of excessive underground density, running parallel to the Himalaya about 400 miles south of their southern boundary. In his Presidential Address to the Indian Science Congress in 1916, Burrard stated that the Himalaya were 80 per cent, compensated, and that taken together with the Gangetic trough there was no extra mass. He denied the adequacy of the contraction theory to explain the mountains and postulated on the contrary a rift extending to a great depth. The crumpling of the hills, apparent at the surface was merely a surface effect.

These interesting deductions, not accepted by all geologists, were derived from consideration of the horizontal attraction of the Himalaya : but the complexity of the subject is apparent. It was not possible to disentangle Himalayan effects from non-Himalayan effects with absolute precision : and, as is usual in such investigation, the scope of the enquiry was greatly extended. Burrard^Js early researches into the Himalayan attraction stimulated similar enquiries outside India. In the United States, Hayford, in 1909, published his account of his determination of the Figure of the Earth from deflection observations, and introduced his hypothesis of universal compensation and isostasy, which has since then been accepted by many geologists and geodesists. Hayford accepted Pratt's conception of compensation, and applied it not only to great mountain ranges as Pratt had done, but also to every topographical feature whether above or below sea-level. He deduced 70 miles as the most probable general depth at which compensation was complete.

Intensity of Gravity.—So far I have referred to the horizontal pull of the Himalaya : and it is to be noted that observations of this have only been made, with few exceptions, at points external to the hills or near to their southern boundary. There are greater technical difficulties in carrying out all the necessary observations far into the hills themselves, but this is now being done as opportunity offers. Precise observation usually requires heavy instrumental equipment, difficult of transport in vast mountain ranges ; and for deflections continuity with the external work is essential. There is however another method of attack, namely, the measurement of the actual force of gravity. This force can be found with great precision by observing the rate of swing of a pendulum. Claurault's celebrated theorem, as subsequently developed, enables us to build up a formula for gravity on a spheroidal earth, and the pendulum observations show anomalies of gravity which can be used in enquiries into the state of affairs below the surface. Properly reduced these anomalies indicate the vertical component of attraction of the neighbouring matter, and the results are less disturbed by outlying causes than are those of the deflections.

Pendulum observations were begun in India in 1865 and terminated in 1871. In the latter year after leaving More, a plateau of altitude 15,400 feet in Ladakh, for a higher station, the observer Captain Basevi lost his life. For many years no other observations were made. The More result would have been of especial interest on this account: but unfortunately a source of error—sway of the pendulum stand—was not foreseen at the time of observation, and it has been impossible to make satisfactory allowance for it subsequently. A new series of pendulum observations were begun in India in 1903 by Major (now Sir Gerald) Lenox Conyngham. The rate of swing of a pendulum depends on the force of gravity and also on its own effective length. This latter varies with temperature and it is only recently that satisfactory observations have been possible unless made in a substantial building, in which temperature variation can be considerably controlled. On this account the observations were formerly restricted to places where bungalows were to be found. In 1925 Major Glennie carried his pendulum observations into Kashmir and to the Deosai plains, thus penetrating the Himalaya to a considerable extent.

Recent Himalayan Results.—On the Deosai plains at an average elevation of 12,800 feet, Glennie found considerable positive anomalies of gravity, indicating that the Himalaya there were not fully compensated. A stratum of ordinary surface density rock, 1,500 feet thick, would be adequate to account for this, indicating that compensation of mass is here about 88 per cent. At other stations to the south and near the Kashmir valley smaller anomalies were found. Moreover there is a preponderance of southerly deflection of the plumb-line, which when taken in conjunction, with results in the Punjab seem to be in contradiction to the gravity results. Still further observations are required to clear up this point.

Such observations will go far to determine the outstanding doubts as to the state of affairs underlying the Himalaya. Up to date they can only be made by a party specially organized for the purpose— such as Major Glennie's : or the general scientific and exploratory expedition of Sir Filippo De Filippi in 1913-14 or that of H. E. H. the Duke of Spoleto, which will be at work in the Karakoram this year. The ordinary pendulum apparatus is heavy and the observation protracted, so that nothing can be done in this way by the ordinary Himalayan traveller. However some difficulties are becoming less formidable than formerly. For example, precise time-observations are no longer necessary, as these can now be replaced by wireless time- signals. The temperature difficulty is removed by the employment of invar pendulums which vary very little in length. Perhaps the time is not far distant when gravity-observations will be within the scope of a moderately-equipped Himalayan expedition. When this is possible we may hope to gain adequate knowledge of the attraction of the Himalaya, and understand more completely the basis on which they rest.

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